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Updated: May 13, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Computing rovibrational levels of methane with curvilinear internal vibrational coordinates and an Eckart frame
Xiao-Gang Wang1, Tucker Carrington
1Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada. xgwang.dalian@gmail.com
Abstract:
We present a new procedure for computing a rovibrational spectrum of a polyatomic molecule and apply it to methane. The Schrödinger equation is solved, numerically exactly, by using a nested contracted basis. Rovibrational wavefunctions are computed in a |v>|JKM> basis, where |v> is a vibrational wavefunction and |JKM> is a symmetric top wavefunction. In turn, the |v> are obtained by solving a vibrational Schrödinger equation with basis functions that are products of contracted bend and stretch functions. At all stages of the calculation we exploit parity symmetry. The calculations are done in internal coordinates that facilitate the treatment of large amplitude motion. An Eckart molecule-fixed frame is used by numerically computing coefficients of the kinetic energy operator. The efficacy of the method is demonstrated by calculating a large number of converged J = 10 methane rovibrational levels in the Tetradecad polyad. No previous calculation of rovibrational levels of methane includes as many levels as we report in this paper.
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